POST UTME AL-HIKMAH UNIVERSITY 2017 Physics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A radioactive sample of $^{238}U$ has a half-life of $4.5 \times 10^9$ years. If the initial activity of the sample is $A_0 = 10^6$ Bq, what is the activity of the sample after $t = 1.5 \times 10^9$ years?
A. \( A = 2.5 \times 10^5 \) Bq
B. \( A = 5.0 \times 10^5 \) Bq
C. \( A = 1.0 \times 10^6 \) Bq
D. \( A = 2.0 \times 10^6 \) Bq
Question 2
A parallel plate capacitor consists of two plates of area $A$ separated by a dis\tance $d$. The capaci\tance is given by $C = \frac{epsilon_0 A}{d}$. If the area of the plates is doubled and the dis\tance between them is halved, what is the new capaci\tance?
A. $\frac{\epsilon_0 A}{d}$
B. $\frac{2\epsilon_0 A}{d}$
C. $\frac{\epsilon_0 A}{d/2}$
D. $\frac{4\epsilon_0 A}{d/2} = 8\frac{\epsilon_0 A}{d}$
Question 3
A ray of light passes from air into a glass slab of re\fractive index $\mu = 1.5$. If the angle of incidence is $30^\circ$, what is the angle of re\fraction?
A. $20^\circ$
B. $30^\circ$
C. $40^\circ$
D. $50^\circ$
Question 4
A particle of mass $m$ is moving in a circular path of radius $r$ with a cons\tant speed $v$. If the particle is subjected to a centripetal force $F_c$, calculate the magnitude of $F_c$.
A. \frac{mv^2}{r}
B. \frac{mv^2}{2r}
C. \frac{mv^2}{3r}
D. \frac{mv^2}{4r}
Question 5
A circuit consists of a resistor of resis\tance $R$ and an inductor of induc\tance $L$ connected in series. The circuit is connected to a battery of emf $V$ and is then disconnected from the battery. If the circuit is then connected to a capacitor of capaci\tance $C$, what is the time cons\tant of the circuit?
A. \( \tau = \frac{L}{R} \)
B. \( \tau = \frac{C}{R} \)
C. \( \tau = \frac{L}{C} \)
D. \( \tau = RC \)
Question 6
A radioactive sample decays with a half-life of $T_{1/2}$. If the initial activity is $A_0$, calculate the activity $A$ after time $t$.
A. A_0e^{-\frac{t}{T_{1/2}}}
B. A_0e^{-\frac{T_{1/2}}{t}}
C. A_0e^{-\frac{t}{2T_{1/2}}}
D. A_0e^{-\frac{2t}{T_{1/2}}}
Question 7
A magnetic field $B$ is directed perp\endicular to a current-carrying wire of length $L$. If the current is $I$, calculate the force $F$ on the wire.
A. ILB
B. \frac{ILB}{2}
C. \frac{ILB}{3}
D. \frac{ILB}{4}
Question 8
A ray of light passes from air into a glass slab of re\fractive index $\mu$. If the angle of incidence is $\theta_i$, calculate the angle of re\fraction $\theta_r$.
A. \sin^{-1}\left\( \frac{\sin\theta_i}{\mu}\right \)
B. \sin^{-1}\left\( \frac{\mu\sin\theta_i}{\mu}\right \)
C. \sin^{-1}\left\( \frac{\sin\theta_i}{\mu^2}\right \)
D. \sin^{-1}\left\( \frac{\mu\sin\theta_i}{\mu^2}\right \)
Question 9
A body of mass $m$ is moving in a circular path of radius $r$ with a speed $v$. If the body is subjected to a centripetal force $F_c = \frac{mv^2}{r}$, what is the work done by this force in moving the body through a dis\tance $s$?
A. $\frac{1}{2}mv^2$
B. $mv^2$
C. $\frac{1}{2}mv^2s$
D. $\frac{1}{2}mv^2s^2$
Question 10
A radioactive sample has a half-life of $T_{1/2} = 10$ years. If the initial activity is $A_0 = 100$ Bq, what is the activity after $t = 20$ years?
A. $50$ Bq
B. $25$ Bq
C. $12.5$ Bq
D. $6.25$ Bq
Question 11
A gas of molecules with mass $m$ and charge $q$ is confined to a box of volume $V$. The gas is heated to a temperature $T$ and then allowed to expand to a volume $V + \Delta V$. What is the change in the internal energy of the gas?
A. \( \Delta U = \frac{3}{2} nR \Delta T \)
B. \( \Delta U = \frac{5}{2} nR \Delta T \)
C. \( \Delta U = \frac{7}{2} nR \Delta T \)
D. \( \Delta U = \frac{9}{2} nR \Delta T \)
Question 12
A simple harmonic motion has a period $T = 2\pi$ s. If the amplitude is $A = 10$ cm, what is the angular frequency?
A. $\frac{1}{2\pi}$ rad/s
B. $\frac{1}{\pi}$ rad/s
C. $\frac{2}{\pi}$ rad/s
D. $\frac{1}{\pi}$ rad/s
Question 13
A parallel plate capacitor has plates of area $A$ and separation $d$. If the electric field between the plates is $E$, calculate the capaci\tance $C$.
A. \frac{A\epsilon_0}{d}
B. \frac{A\epsilon_0}{2d}
C. \frac{2A\epsilon_0}{d}
D. \frac{A\epsilon_0}{3d}
Question 14
A solid cylinder of radius $R$ and height $H$ floats in a liquid of density $\rho_l$ with its axis vertical. If the cylinder is displaced slightly from its equilibrium position, it oscillates about its equilibrium position with a frequency $f$. What is the value of $f$ in terms of $R$, $H$, and $\rho_l$?
A. \( f = \frac{1}{2\pi} \sqrt{\frac{g\rho_l}{R\rho_s}} \)
B. \( f = \frac{1}{2\pi} \sqrt{\frac{g\rho_l}{H\rho_s}} \)
C. \( f = \frac{1}{2\pi} \sqrt{\frac{g\rho_s}{R\rho_l}} \)
D. \( f = \frac{1}{2\pi} \sqrt{\frac{g\rho_s}{H\rho_l}} \)
Question 15
A parallel plate capacitor has plates of area $A$ and separation $d$. The capacitor is connected to a battery of emf $V$ and is then disconnected from the battery. If the capacitor is then connected to a resistor of resis\tance $R$, what is the time cons\tant of the circuit?
A. \( \tau = \frac{V}{I} \)
B. \( \tau = \frac{V}{R} \)
C. \( \tau = \frac{V}{A} \)
D. \( \tau = RC \)

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